Computer Science 102

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Computer Science 102

• Into to Computational Modeling
• Spring 2009
• Special Topics Programming in Matlab

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Matlab

• An integrated programming and graphical
  environment
• Interpreted interactive get answer immediately
• Also supports saving and loading large programs
• Student version available for 100 from
  mathworks.com
• Free, open-source equivalent Octave
• http//www.gnu.org/software/octave

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Matlab

• Questions
• Why Matlab vs. lower-level (C / Java / Python)
  language?
• Why Matlab vs. a similar package (Mathematica,
  Maple) ?

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Matlab vs. C/Java/Python

• Abstraction We should be able to ignore
  low-level details, such as memory management
  (required in C)
• Expressiveness
• Simple (primitive) operations like add, subtract,
  multiply, divide, should work on entire matrices
  (tables) at once, without having to consider
  individual elements
• Common operations like S (sum over elements)
  should be built into the language, so we dont
  have to code them ourselves.

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Expressiveness
gtgt a rand(3) a 0.7577 0.6555
0.0318 0.7431 0.1712 0.2769 0.3922
0.7060 0.0462 gtgt b rand(3) b
0.0971 0.3171 0.4387 0.8235 0.9502
0.3816 0.6948 0.0344 0.7655 gtgt c a
b c 0.8549 0.9726 0.4706
1.5666 1.1214 0.6585 1.0871 0.7405
0.8117

• Generate two matrices of uniformly distributed
  random numbers and add them

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Expressiveness

• Where one matrix is greater than another, set
  the first matrix to zero

gtgt a(agtb) 0 a 0 0
0.0318 0.7431 0.1712 0.2769 0.3922
0 0.0462
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Matlab vs. Maple/Mathematica

• Features
• Matlab Numerical (linear algebra)
• Maple, Mathematica Symbolic (calculus)

from http//www.physicsforums.com/archive/topic/
t45208_Matlab_vs_Maple_vs_Mathematica.html
... Matlab is excellent for manipulating data, or
dealing with any sort of matrix
calculations.. From my experience Mathematica is
ideal when it comes to symbolics such as
differentiation and integration. I've seen a few
cases where Mathematica blows Maple out of the
water when one compares the types of integrals
they can evaluate. Maple and Matlab have the
best graphics in my opinion. In both of them you
are allowed to rotate 3D graphics and zoom in on
the spot (2D) in realtime. In Mathematica things
are little more complicated, which often
elicits frustration. With Mathematica, in order
to zoom, you must change the window that you are
plotting with.
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The Matlab Environment

• Integrated Development Environment
• Editor Command Window (Interpreter)

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Expressions and Commands

• Anything you type into the Matlab interpreter (gtgt
  prompt) is a statement.
• An expression is a statement that provides all
  the information needed to invoke (perform) a
  computation.

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Expressions and Commands

• The interpreter responds by evaluating the
  expression
• Simplest example is a constant value
• gtgt 4
• ans 4

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Expressions and Commands

• An expression typically contains
• an operator , , -, /, , sin, cos, sqrt
• one or more inputs (a.k.a. arguments a.k.a.
  operands)
• Two different styles (same result)
• Functional plus(3, 2)
• Infix 3 2

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Expressions and Commands

• As in arithmetic notation,
• build compound expressions from simple
  expressions 3 2 5 / sin(pi/3)
• use Order of Operations (PEMDAS) and parentheses
  to disambiguate
• (3 2) 5 / sin(pi/3)

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Expressions and Commands

• Good programmers don't
• assume that others know order of operations
• want to waste time using o.o.o. to disambiguate
  code they're reading

• So use parens if there's a reasonable chance of
  ambiguity

1 2 3 / 4
1 ((2 3) / 4)
Programs should be written primarily to be read
and understood by people D. Knuth.
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Changing State Assignment

• Just as a system (health, airplane, particle) can
  have a state, so can a computation.
• State of computation is contents of computer's
  memory (RAM).
• We change this state (and hence state of system
  we're modeling) by assigning values to variables

gtgt altitude 13000 gtgt temperature 98.7 gtgt area
pi radius2
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Changing State Assignment

• More generally

name
expression
gtgt

• Variable name must start with a letter or
  underscore (_), and can then contain letters,
  numbers, and underscores

a
radius
buffalo66
cost_of_living
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Changing State Assignment

• This notation differs from arithmetic, where it
  makes no sense to say, for example, x x 1
• In addition to state, variables help us to
• write general formulas
• gtgt c sqrt(a2 b2)
• avoid repeating computation of useful
  intermediate values.
• We should avoid repeating the same computation
  (code), because if there's a bugg in it, we have
  to fix it multiple times.
• We should avoid repeating the same computation
  (code), because if there's a bugg in it, we have
  to fix it multiple times.

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Changing State Assignment

• E.g., gravitational force F of moon at location
  (x, y, z) w.r.t. center of earth

all contain
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Changing State Assignment
all contain

• So...

gtgt pos_to_force -GmM/((x2 y2
z2)(3/2)) gtgt Fx xpos_to_force gtgt Fy
ypos_to_force gtgt Fz zpos_to_force
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Help!

• All Matlab operators have built-in help
• gtgt help cos
• COS Cosine.
• COS(X) is the cosine of the elements of X.
• See also ACOS, COSD.

• Unbroken block of comments at top of your own
  code gets reported as help

gtgt help simon_lab1 Simon Levy, CSCI 121, Jan.
04,2005 Lab 1 Polynomial Curve Fitting
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What if you cant remember the exact name?
gtgt lookfor circle WRLDTRV Show great circle
flight routes around the globe.
ipexConformalShowCircles Plot packed circles
before/after transformation. CIRCCIRC Find the
intersections of two circles in cartesian
space GC2SC Converts a great circle definition
to a center and radius GCWAYPTS Computes
equally spaced waypoint coordinates along a great
circle GCXGC Computes the intersection points
between two great circles . . .
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Functions The Basis of Computing

• Most of what we do in Matlab (or any language)
  involves writing and using functions.
• Like a function in math, a Matlab function has
  one or more inputs (arguments) and an output
  (return value).
• Each function is stored in its own document (.m
  file)
• We can call functions directly from the command
  prompt, and functions can call each other.

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Example Hypotenuse of Right Triangle
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Variable Names Are Arbitrary But Should Make Sense
required
function foo bar(baz, moo) foo sqrt(baz2
moo2)
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A Functions Variables Are Private (Hidden)
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Programming to an API

• It is rare to build an entire software project
  from scratch.
• Instead, we reuse our own or others code.
• So we have to know how to invoke (call) existing
  code.
• Application Programming Interface specifies how
  to do this
• Simplest form is what we get when call help on a
  function

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Requirement Specification via Stub Functions

• Stub function is like an API for something not
  yet written